Polaronic enhancement in the ground-state energy of an electron bound to a Coulomb impurity in a parabolic quantum dot

Using the Feynman-Haken variational path-integral formalism we obtain the polaronic correction to the ground-state energy of an electron bound to a positive Coulomb impurity in a polar semiconductor quantum dot with parabolic confinement in both two and three dimensions. We perform calculations for the entire range of the electron-phonon coupling constant and the Coulomb binding parameter and for arbitrary confinement length. We apply our results to several semiconductor quantum dots and show that the quantum-dot enhancement in the polaronic correction in some of these dots can be very large.